USING IDEALS TO PROVIDE A UNIFIED APPROACH TO UNIQUELY CLEAN RINGS

DOI10.1017/S1446788713000591zbMath1302.16035OpenAlexW2011485760MaRDI QIDQ5415975

Sharad Hegde, Veereshwar A. Hiremath

Publication date: 19 May 2014

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788713000591

zbMATH Keywords

idempotentsideal extensionssemipotent ringsuniquely clean ringsnil-clean ringsnil-clean elementsuniquely \(I\)-clean rings

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Generalizations of commutativity (associative rings and algebras) (16U80) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (2)

Lifting properties of formal triangular matrix rings ⋮ ON LIFTING OF STABLE RANGE ONE ELEMENTS

Cites Work

• Strong lifting splits.
• Bass's first stable range condition
• Rings with many idempotents
• Strongly clean triangular matrix rings over local rings.
• On Uniquely Clean Rings
• RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT

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